Question

1. cm 13 cm 5 cm b

Explanation:

Step1: Apply Pythagorean theorem

Let the side - length of the unknown square be $b$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 5$ and $c = 13$.
So $5^{2}+b^{2}=13^{2}$.

Step2: Calculate the values

First, calculate $5^{2}=25$ and $13^{2}=169$. Then the equation becomes $25 + b^{2}=169$.
Subtract 25 from both sides: $b^{2}=169 - 25=144$.

Step3: Solve for $b$

Take the square - root of both sides. Since $b>0$ (as it represents a length), $b=\sqrt{144}=12$.

Answer:

12